$f(x) = -7x^{2}+2(h(x))$ $h(x) = -5x^{2}-6x+6$ $g(t) = -4t-4+h(t)$ $ g(h(-1)) = {?} $
Solution: First, let's solve for the value of the inner function, $h(-1)$ . Then we'll know what to plug into the outer function. $h(-1) = -5(-1)^{2}+(-6)(-1)+6$ $h(-1) = 7$ Now we know that $h(-1) = 7$ . Let's solve for $g(h(-1))$ , which is $g(7)$ $g(7) = (-4)(7)-4+h(7)$ To solve for the value of $g$ , we need to solve for the value of $h(7)$ $h(7) = -5(7^{2})+(-6)(7)+6$ $h(7) = -281$ That means $g(7) = (-4)(7)-4-281$ $g(7) = -313$